JP4427258B2 - Signal processing method, signal processing program, recording medium recording this signal processing program, and signal processing apparatus - Google Patents

Description

を、スプラインのエネルギー、
【数２】

を最小にするという条件下で、最小にすることで実現する。すなわち、スプラインフィルタは、
【数３】

としたとき、I(s)を最小にするスプライン関数sを求めることによって実現される。ただし、λはラグランジェの未定乗数である。
【００２９】
いま、w_k（k＝0，1，・・・，n-1）を各測定点における残差に対する重みとすれば、重み付きのスプラインフィルタに対応した式、
【数４】

が得られる。
【００３０】
ここで、スプライン関数ｓを定ピッチで離散化し、第２項を、
【数５】

とすると、
【数６】

【００３１】
となる。ただし、
【数７】

とする。したがって、I（ｓ）を最小にする離散化スプラインの値ｓ_kは、
【数８】

を満足する。
【００３２】
式（６）においてI（ｓ）を最小にするスプライン関数で重み付きスプラインフィルタを定義する。
【００３３】
ここで、非周期的測定データに対する重み付きスプラインフィルタの行列表現を考えると、非周期的な測定データにおいては、境界条件を
【数９】

とすると、
【数１０】

であるので、
【数１１】

とおくことにより、非周期的データに対する重み付きスプラインフィルタの行列表現は、
【数１２】

で与えられる。
【００３４】
但し、
【数１３】

である。
【００３５】
次に、周期的測定データに対する重み付きスプラインフィルタの行列表現を考えると、周期的な測定データにおいては、周期境界条件の式を
【数１４】

とすると、
【数１５】

であるから、
【数１６】

として、周期データに対する重み付きスプラインフィルタの行列表現は、
【数１７】

で与えられる。
【００３６】
ここで、スプラインフィルタの振幅特性と位相特性を検討する。
重みW=I（単位行列）としたスプラインフィルタの式、
【数１８】

を、z^-1がΔx分の遅延を意味することに注意し、z変換で表現すると、
【数１９】

となる。
【００３７】
スプラインフィルタの伝達関数H(z)は、
【数２０】

で与えられる。振幅特性と位相特性を調べるために、
【数２１】

とおくと、
【数２２】

となる。
【００３８】
ここで、
【数２３】

であるから、
【数２４】

となり、振幅特性は、
【数２５】

となる。
【００３９】
一方、位相特性は、
【数２６】

となり、スプラインフィルタは、位相補償フィルタであることがわかる。
【００４０】
一例として、カットオフ周波数ω＝ω_Cで50％減衰のフィルタを実現する場合、振幅特性において、
【数２７】

とすれば良く、これにより定数αが次式で与えられる。
【数２８】

カットオフ周波数ω＝ω_Cで50％減衰のフィルタの伝達特性（振幅特性、位相特性）を図５に示す。
【００４１】
次に、このように定義された重み付きスプラインフィルタの解法を検討する。
重み付きスプラインフィルタの行列表現、
【数２９】

の左辺係数行列、
【数３０】

は、対称行列である。
【００４２】
そこで、Mを修正コレスキー（Choleskey）法により下三角行列Lと対角行列Dに分解すると（行列Mが疎行列であることを利用すれば、行列の分解は非常に効率的に行うことが出来る。）、
【数３１】

となり、重み付きスプラインフィルタは、
【数３２】

と表される。
【００４３】
ここで、
【数３３】

とすれば、
【数３４】

となる。
【００４４】
ここで、Lは下三角行列であるから容易にXを求めることが出来る。さらに、
【数３５】

なる関係より、求まったXから容易にSを求めることができる。
実際の適用にあたっては、
【数３６】

となる場合が有り得ることから、行列Mが特異になる可能性がある。
【００４５】
従って、理想的には特異値分解法により解くことが好ましいが、特異値分解法を使った場合、大容量の記憶装置と多大の計算処理時間が必要となる。ところが、現実の測定データに適用することを考えた場合、行列Mが特異になることは非常にまれであり、行列Mが特異になっている状態では測定データ自体に問題を抱えていると推測される。そこで、本件発明においては、行列Mが特異になっている場合でも、なんらかの解答を出力可能な、ギルとマーレイ（Gill-Murray）の修正コレスキー（Choleskey）法を適用することで、計算効率の確保と特異行列対策を両立させる。
【００４６】
以上のように解法に裏付けられた重み付きスプラインフィルタが導出されたので、以下、重みWを更新しながら収束条件を満足するまで繰り返し計算処理を行うことによって、ロバストスプラインフィルタが実現される。
図１は、その第１の処理手順を示すフローチャートであり、図２は、ロバストスプライン処理を実行する装置の機能ブロック図である。この処理にあたっては、まず、測定データを入力する測定データ入力ステップと、重み付きスプラインフィルタ式を選定する選定ステップ（ＳＴ３）が実行される。
【００４７】
測定データ入力ステップでは、測定機などから入力手段１により測定データを入力してコンピュータなどの記憶装置２に格納するステップＳＴ１と、記憶された測定データの内、局所的に離隔した特異点データを特異点データ削除手段３にて削除するステップＳＴ２が実行される。
ここでは、測定データは粗さ測定機で測定された一次元時系列データであるとする。すなわち、例えば、表面粗さ測定機などにおいて、測定子を一方向（ｘ方向）に移動させた場合に、ｘ方向の所定ピッチで粗さデータｙを取得したような場合を意味する。また、特異点データであるか否かの判定としては、測定データの最小二乗曲線からの離隔量が所定値以上、かつ、所定区間巾以下、であるか否かで容易に判定することが出来る。
【００４８】
その後、選定ステップＳＴ３において、判定手段４にて測定データが非周期的であるか周期的であるかを判定し、この判定に従って重み付きスプラインフィルタ式を選定する。より具体的には、測定データが非周期的であるか周期的であるかによって（１２）式を用いるか、（１７）式を用いるかを判定する。
次に初期化処理（ＳＴ４）を行うが、ここでは、図示したように、W＝I（単位行列）としたスプラインフィルタ処理の出力値の初期値S⁰を求める（非ロバストなスプラインフィルタ計算）。
次に、測定データYとS^m（mは繰り返しのステップを示す。）とから後述する方法で重み調整手段５により重みW^mを調整して決める（ＳＴ５）。
【００４９】
その後、スプラインフィルタ出力算出手段６において重み付きスプラインフィルタ、
【数３７】

からスプラインフィルタ出力S^m+1を求める（ＳＴ６）。
ここで、後述する重みの収束判定（ＳＴ７）を収束判定手段５１にて行って、収束条件が成立していなければ、mを更新して（m＝m+1）（ＳＴ１０）、再度重みW^mを調整する（ＳＴ５）。
【００５０】
収束条件が成立していれば（ＳＴ７：ＹＥＳ）、繰り返し処理を終了して、ロバストスプラインフィルタの出力値S^mを得て（ＳＴ８）、スプライン曲線が出力手段７に出力される。
以上の処理において、重みW^mを調整して決める方法として（ＳＴ５）、適合型バイウエイト（Biweight）法を用いて次のように決定する。
【数３８】

【００５１】
ここで、σを残差の標準偏差として、
【数３９】

【数４０】

とする。
【００５２】
また、ＳＴ７における収束条件としては、重みの変化が十分小さくなり、以下に示す式を満足した時点で繰り返し処理を打ち切る。
【数４１】

【００５３】
一次元時系列データに対して、この第１実施形態におけるロバストスプラインフィルタ処理による信号処理方法を実施した例を図３に示す。ここではスパイクノイズを付加した測定データを対象として、通常のスプラインフィルタ処理を施した結果のスプライン曲線と、本件発明のロバストスプラインフィルタ処理を施した結果のスプライン曲線の両方を重ねて表示したものである。この図から明らかなように、スプラインフィルタによる結果が、スパイクノイズによる変化を受けているのに対して、ロバストスプラインフィルタによる結果では、本来の形状に沿ったスプライン曲線が得られている。また、図３（Ａ）からもわかるように、ゆるやかなうねりをもった形状に対する追随性も良好である。
【００５４】
この方法によれば、次の効果が期待できる。
（１）スプラインフィルタのロバスト化が容易に実現できるので、測定データ始点あるいは測定データ終点領域における変形を防止でき、測定データに含まれる周期の長いうねり成分に対する追随性あるいはノイズ成分に影響されずに測定データに含まれる形状を抽出できるので形状追随性も良好なフィルタ処理が可能となり、測定データの信頼性がより向上する。
（２）測定データに含まれた局所的に離隔した特異点データを削除できるので、ロバストスプラインフィルタ処理の信頼性が更に向上する。
【００５５】
（３）重み付きスプラインフィルタ式により算出されるスプライン曲線からの測定データの離隔量が大きいほどその重みが小さくなるので、測定データに含まれる異常データの影響を受けないロバストスプラインフィルタ処理が可能となる。
（４）繰り返しループ処理における重みの変化が所定値以下となった場合に、重みが収束したと判定できるので、不必要な繰り返しループによる処理を防止でき、ロバストスプラインフィルタ計算処理時間を短縮できる。
【００５６】
（第２実施形態）
次に、ロバストスプラインフィルタを実現する第２の処理手順を説明する。この処理手順は、前記第１の処理手順と同一であるが、用いる計算式が異なる。
すなわち、重み付きスプラインフィルタの式、
【数４２】

を変形して、
【数４３】

とする。
【００５７】
ここで、繰り返しステップmにおいて、
【数４４】

を用いる。
この第２の処理手順の特徴は、前記第１の処理手順の効果（１）から（４）に加えて更に次の効果が期待できる。
【００５８】
（５）左辺の係数行列、
【数４５】

が繰り返しステップにおいて常に同値となるので、全体としてロバストスプラインフィルタ計算処理時間が短縮化される場合がある。
【００５９】
（第３実施形態）
次に、本発明の信号処理方法にかかる第３実施形態として、二次元的に測定された二次元データである測定データに対する信号処理方法について説明する。ここで、二次元データである測定データとは、例えば、三次元測定機などにおいて、Z座標一定のもとで被測定物の輪郭曲面を所定ピッチで測定して取得された（ｘ、ｙ）座標値等を意味する。あるいは、平面的に描かれた図形をスキャナで読み込んだ場合のデータ等を意味する。つまり、第１実施形態においては、処理の対象はｙ座標だけであったのに対して、第３実施形態では、ｘ座標およびy座標の両者を処理の対象とする。
第３実施形態の基本的構成は第１実施形態と同様であるが、スプライン曲線ｓを求めるための出発の式である式（６）に対応する式に特徴がある。
【００６０】
第３実施形態では、スプラインのエネルギーを最小にする条件のもとで、測定データ（ｘ_k、ｙ_k）と、この測定データ（ｘ_k、ｙ_k）に対応するスプライン曲線ｓ上の点（ｓ_x（ｘ_k、ｙ_k）、ｓ_y（ｘ_k、ｙ_k））とのＸ方向およびＹ方向の距離の二乗和を最小にするスプライン曲線を求める。すなわち、前記の付帯条件のもとで次の式で表されるI（ｓ）を最小にするスプライン関数ｓを求める。
【００６１】
【数４６】

【００６２】
ただし、右辺第２項において、ラプラシアンの２次近似を次のように表す。
【００６３】
【数４７】

【００６４】
そして、ｘ成分、ｙ成分ごとにそれぞれ第１実施形態で説明した重み付きスプラインフィルタを実行する（（式３７）を参照）。
ここで、定数αについては、測定経路に沿ったサンプリングピッチΔｌおよびカットオフ波長λ_c’から次の式で与えられる。
【００６５】
【数４８】

【００６６】
すると、二次元測定データに関する各区間におけるスプライン曲線を導出するスプラインフィルタが実現される。
さらに、重みWを更新して収束条件（式４１）を満たすまで処理を繰り返すロバストスプラインフィルタにおいては、（式３８）における（ｙ_k−ｓ_k ^m）を次の式で与えられる二点間距離とする。すなわち、測定データ（ｘ_k、ｙ_k）と、この測定データ（ｘ_k、ｙ_k）に対応するスプライン曲線ｓ上の点（ｓ_x（ｘ_k、ｙ_k）、ｓ_y（ｘ_k、ｙ_k））との距離とする。
【００６７】
【数４９】

【００６８】
（式４９）を準用した（式３８）により算出された重みWの収束を（式４１）で収束判定する。重みWが収束したところで、出力値S^m（スプライン関数）から測定データに対応するスプライン曲線を得る。このスプライン曲線は、出力手段に出力される。
【００６９】
図４（Ａ）に、正葉線にスパイクノイズを付加した入力データに対して、スプライン処理を施したものと、ロバストスプライン処理を施したものとを比較して示す。図４（Ａ）より、単なるスプライン処理では、スパイクノイズに引きずられてしまっているのに対して、ロバストスプライン処理では、スパイクノイズを抑えたロバスト（頑健）な結果が得られることがわかる。図４（Ｂ）に、エアフォイルにスパイクノイズを付加した入力データに対して、スプライン処理を施したものと、ロバストスプラインを施したものとを示すところ、結果は図４（Ａ）と同様である。
【００７０】
この第３実施形態においては、前記第１実施形態と第２実施形態における効果（１）から（５）に加えて、更に次の効果を奏する。
（６）測定データが直交座標における二次元データである場合に、スプライン曲線からの測定データの離隔量は、各軸毎の成分（例えば、Ｘ軸成分、Ｙ軸成分など）の自乗和に基づいて決定するので、離隔量の算出が容易に行える。従って、各測定データの重みを決定することが容易になる。
【００７１】
（７）測定データが二次元データの場合であっても、各軸の成分毎（例えばＸ軸成分、Ｙ軸成分など）に重み付きスプラインフィルタ計算を行った結果に基づいてスプラインフィルタ出力を得ることが出来るので、複雑な曲線であっても計算処理が単純化でき、測定データに対するロバストスプラインフィルタ計算処理時間の短縮化が可能になる。
【００７２】
（８）被測定物を二次元平面内で倣い測定して二次元データを得て、これを測定データとして入力する場合においても、測定経路に沿って所定間隔で測定データが入力されるので、例えばＸ軸方向に所定間隔で測定データを入力する場合などに比べて形状変化点（例えば直線から円弧への変化点や段差の境界点など）をより正確に捉えることが出来る。つまり、形状判断の誤りなどを防止でき、信頼性の高い測定データ入力が可能になる。
【００７３】
（第４実施形態）
次に、本発明の信号処理方法にかかる第４実施形態として、三次元的に測定された三次元データである測定データに対する信号処理方法について説明する。ここで、三次元データである測定データとは、例えば、三次元測定機などにおいて、被測定物表面を所定ピッチで測定して取得された（ｘ、ｙ、ｚ）座標値等を意味する。つまり、第１実施形態においては、処理の対象はｙ座標だけであったのに対して、第４実施形態では、ｘ座標、y座標およびｚ座標の三者を処理の対象とする。
第４実施形態の基本的構成は第１実施形態と同様であるが、スプライン曲線ｓを求めるための出発の式である式（６）に対応する式に特徴がある。
【００７４】
第４実施形態では、スプラインのエネルギーを最小にする条件のもとで、測定データ（ｘ_k、ｙ_k、ｚ_k）と、この測定データ（ｘ_k、ｙ_k、ｚ_k）に対応するスプライン曲線ｓ上の点（ｓ_x（ｘ_k、ｙ_k、ｚ_k）、ｓ_y（ｘ_k、ｙ_k、ｚ_k）、ｓ_z（ｘ_k、ｙ_k、ｚ_k））とのＸ方向、Ｙ方向およびＺ方向の距離の二乗和を最小にするスプライン曲線を求める。すなわち、前記の付帯条件のもとで次の式で表されるI（ｓ）を最小にするスプライン関数ｓを求める。
【００７５】
【数５０】

【００７６】
ただし、右辺第２項において、ラプラシアンの２次近似は、第３実施形態に倣って表される。
そして、ｘ成分、ｙ成分、ｚ成分ごとにそれぞれ第１実施形態で説明した重み付きスプラインフィルタを実行する（（式３７）を参照）。なお、定数αについては、三次元空間における測定経路に沿ったサンプリングピッチΔｌおよびカットオフ波長λ_c’により（式４８）に倣って定義される。
【００７７】
すると、三次元測定データに関する各区間におけるスプライン曲線を導出するスプラインフィルタが実現される。
さらに、重みWを更新して収束条件（式４１）を満たすまで処理を繰り返すロバストスプラインフィルタにおいては、（式３８）における（ｙ_k−ｓ_k ^m）を次の式で与えられる二点間距離とする。すなわち、測定データ（ｘ_k、ｙ_k、ｚ_k）と、この測定データ（ｘ_k、ｙ_k、ｚ_k）に対応するスプライン曲線ｓ上の点（ｓ_x（ｘ_k、ｙ_k、ｚ_k）、ｓ_y（ｘ_k、ｙ_k、ｚ_k）、ｓ_z（ｘ_k、ｙ_k、ｚ_k））との距離とする。
【００７８】
【数５１】

【００７９】
そして、（式５１）を準用した（式３８）により算出された重みWの収束を（式４１）で収束判定する。重みWが収束したところで、出力値S^m（スプライン関数）から測定データに対応するスプライン曲線を得る。このスプライン曲線は、出力手段に出力される。
【００８０】
この第４実施形態においては、前記第１実施形態と第２実施形態における効果（１）から（５）に加えて、次の効果を奏する。
（９）第３実施形態における効果（６）から（８）を更に三次元データに対して奏することができる。従って、測定データが三次元データであっても、ロバストスプラインフィルタの計算処理時間を増大させることなく、計算負荷を低減することができる。
【００８１】
（変形例１）
本発明の信号処理方法の変形例について説明する。第１実施形態においては、収束判定された時点におけるスプライン曲線をそのまま信号処理結果として出力する例を示したが、この変形例では、もう一度スプライン曲線を求め直し、その結果を信号処理結果として出力する。
【００８２】
図６に、図１のスプライン曲線出力（ＳＴ９）の変形例を示す。
ここでは、まず取得した出力値Ｓ^mを入力する（ＳＴ９１）。その後、再計算を行うか否かを判定する（ＳＴ９２）。例えば、高精度で信号処理結果を得たい場合はＹＥＳを、既に充分な精度で結果が得られたと判断するときはＮＯを、オペレータがその時点で指定すれば良い。あるいは、前もって指定しておくことも出来る。
再計算を行わない場合は（ＮＯ）、出力値Ｓ^mのスプライン曲線を出力手段７によって出力する。再計算を行う場合は（ＹＥＳ）、前もって設定された所定値を超える重みを１に更新する（ＳＴ９３）。つまり、所定値を超えた重みを持つ測定データは有効データであると判断して、スプライン計算処理への寄与度を１００％とする。
その後、更新された重みに基づいて重み付きスプラインフィルタ計算を行って出力を得る（ＳＴ９４）。ここで得られたスプライン曲線を信号処理結果として出力手段７から出力する（ＳＴ９５）。
【００８３】
この変形例は、第１実施形態から第４実施形態においても実施できるので、効果（１）から（９）の他、次の効果を奏することができる。
（１０）収束判定ステップにおいて重みが収束したと判定された時点の重みが所定値を超える場合にその重みを１に更新し、再度スプラインフィルタ出力を得て、その結果を信号処理結果として出力することができる。つまり、重み調整ステップとスプラインフィルタ出力算出ステップとを繰り返して重みが収束したと判定された時点において、その重みが所定値を超える点の測定データは有効データと見做してその重みを１に更新した後、再度スプラインフィルタ出力を得ることができるので、測定データに対するロバストスプラインフィルタ計算が、より確実に行える。そして、その結果を信号処理結果として出力するので、測定データに含まれる本来の形状成分に対して十分誤差の小さいスプライン曲線を求めることができるので、形状追随性の良いロバストスプラインフィルタ処理が可能となる。
【００８４】
以上、本発明について好適な実施形態を挙げて説明したが、本発明は、この実施形態に限られるものではなく、本発明の要旨を逸脱しない範囲での変更が可能である。
たとえば、これらの各実施形態に限らず、三次元粗さデータ、輪郭形状測定機による測定データ、真円度測定機で測定されたデータ、三次元測定機で測定された形状データ、画像測定機で測定されたデータなどのいずれであっても、本発明を実施できる。
【００８５】
また、測定データの収集が接触式のセンサか、非接触式のセンサであるか否かも問わず、さらに、被測定物の表面性状データに限らず、時系列的に発生する電気信号データなどであっても本発明を実施できる。
さらに、本実施形態においては、測定データは一旦、記憶装置に格納される場合に限って説明したが、測定データが収集される毎に、いわゆるリアルタイムで計算処理を行う場合であっても本発明を実施できる。
【００８６】
さらに、本発明の信号処理方法をコンピュータに実行させる信号処理プログラムとしてもよく、この信号処理プログラムは、CD-ROMなどの可搬形の記憶メディアを用いて、各種のコンピュータで実行可能な形で格納することができる。また、この信号処理プログラムは、機械言語に翻訳されるコンパイル形式であっても、あるいは中間言語に翻訳されるインタプリタ形式であっても良い。
【００８７】
また、コンピュータに前記信号処理プログラムを実行させて信号処理装置を構成することが出来る。すなわち、測定データ入力ステップを実行させて測定データ入力手段を、選定ステップを実行させて選定手段を、初期化ステップを実行させて初期化手段を、重み調整ステップを実行させて重み調整手段を、スプラインフィルタ出力算出ステップを実行させてスプラインフィルタ出力算出手段を、収束判定ステップを実行させて収束判定手段を、出力ステップを実行させて出力手段を構成し、これによって信号処理装置を構成できる。
【００８８】
【発明の効果】
以上述べたように、本発明によれば、ロバストスプラインフィルタによるフィルタ処理を施すことのできる信号処理方法を高速、かつ、高精度で行うことができる。
【図面の簡単な説明】
【図１】本発明の信号処理方法に係る第1実施形態において、信号処理手順を示すフローチャートである。
【図２】前記第1実施形態において、信号処理を行う装置の機能ブロック図である。
【図３】前記第1実施形態において、一次元時系列データに対してスプライン処理の結果とロバストスプライン処理との結果とを比較する図である。
【図４】本発明の第３実施形態において、スプライン処理の結果とロバストスプライン処理の結果とを比較する図である。
【図５】本発明に係る信号処理方法に係る伝達特性を示す図である。
【図６】本発明の変形例を示すフローチャートである。
【符号の説明】
３ 特異点データ削除手段
５ 重み調整手段
６ スプラインフィルタ出力算出手段[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a signal processing method, and more particularly to a signal processing method for filtering data obtained by measuring surface properties such as dimensions, shapes, swells, and roughness of an object to be measured.
[0002]
[Background]
A three-dimensional measuring machine for measuring the three-dimensional shape of the object to be measured, a contour shape measuring machine and an image measuring machine for measuring a two-dimensional contour shape, a roundness measuring machine for measuring roundness, and a surface of the object to be measured. 2. Description of the Related Art A surface texture measuring instrument that measures the contour shape, roughness, undulation, etc. of the surface of an object to be measured, such as a surface roughness measuring instrument that measures swell and roughness, is known. These collect the measurement data of the surface of the object to be measured by relatively moving the contact type or non-contact type sensor and the object to be measured.
[0003]
The measurement data collected in this way usually includes disturbance components such as noise.
As the disturbance component, there are many electrical and magnetic induction noises including high-frequency components. For example, when it is desired to obtain the contour shape of the surface of the object to be measured, components such as surface roughness and swell can be disturbance components.
In order to remove such disturbance components as necessary, the measurement data is filtered to remove, for example, high-frequency components.
The simplest configuration for filtering for this purpose is a time constant circuit composed of a resistor and a capacitor when the measurement data is an analog signal. These time constant circuits usually generate phase distortion. For this reason, the filtered measurement data has a drawback that the information on the surface shape cannot be accurately reflected due to, for example, rounding at a location where the surface shape of the object to be measured changes rapidly.
[0004]
On the other hand, there is a method in which measurement data is converted from an analog signal to a digital signal, and the digital signal is filtered by a filter processing program of a computer.
By using this filter processing program, filter processing having performance equivalent to that of the time constant circuit can be performed, and filter processing that does not generate phase distortion, such as a Gaussian filter, can be easily performed.
[0005]
However, these Gaussian filters, 2CR filters, and the like have a problem in that deformation occurs in the measurement data start point or measurement data end point region, and the followability to the wavy component having a long period included in the measurement data is not sufficient.
In addition, if the measurement data includes abnormal data that changes rapidly locally, there is a problem that the data after filtering is locally deformed due to the influence of the abnormal data. .
[0006]
[Problems to be solved by the invention]
To avoid these problems, spline filters are used.
It is known that this spline filter can suppress the occurrence of deformation in the data start point or data end point region, and also has good followability with respect to a wavy component having a long period included in measurement data.
[0007]
However, on the other hand, the spline filter may have a large change in the filter processing result with respect to slight fluctuations in the measurement data. In order to solve this problem, for example, the invention disclosed in Japanese Patent Application Laid-Open No. 9-79992 obtains a spline curve after oversampling and filtering, and determines the magnitude of an error between the spline curve and interpolation data. The spline curve is obtained, and these curves are added. However, since this method generates data that did not originally exist as measurement data by oversampling, there is a problem in terms of reliability when applied to measurement data such as the surface properties of the object to be measured. It was.
[0008]
Further, the invention disclosed in Japanese Patent Application Laid-Open No. 8-278343 removes the power of the high-frequency component of the signal waveform when it exceeds a predetermined value, and then divides the signal waveform into a plurality of sections. It is configured to perform spline smoothing. However, this method also combines the data after performing spline smoothing for each section, so it is difficult to predict in terms of smoothness at the connection point, and it is applied to measurement data such as the surface properties of the object to be measured. However, there was still a problem in terms of reliability.
[0009]
The present invention has been made to solve such problems, and provides a highly reliable signal processing method that can be applied to measurement data such as surface properties of an object to be measured while retaining the characteristics of a spline filter. In addition, a signal processing program, a recording medium on which the signal processing program is recorded, and a signal processing apparatus are provided.
[0010]
[Means for Solving the Problems]
  In order to achieve the above object, the present invention providesObtained by measuring the surface properties of the object to be measuredIn a signal processing method for filtering measurement data, a measurement data input step for inputting the measurement data along a measurement path; and the measurement dataDetermines whether or not is periodic and follows this determinationA selection step of selecting a weighted spline filter equation, an initialization step of obtaining a weight of the measurement data by a unit matrix to obtain an initial value of the spline filter output, and a weight adjustment step of adjusting and determining the weight of the measurement data A spline filter output calculating step for obtaining a spline filter output using the weight determined in the weight adjusting step, a convergence determining step for determining convergence of the weight, and outputting a signal processing result based on the spline filter output An output step, and the weight determined in the weight adjustment step is determined by a separation amount of measurement data from a spline curve calculated by the weighted spline filter equation and a variable determined based on the separation amount. The smaller the distance, the smaller the adjustment If the weight is determined to be non-convergence in the convergence determination step, the weight is updated, the weight adjustment step and the spline filter output calculation step are repeated, and the measurement data is robust spline. A filtering process is performed.
[0011]
According to the present invention, a weighted spline filter equation is selected, and a spline curve as a spline filter output is repeatedly calculated while sequentially updating the weight based on the selected spline filter equation. Robust spline filter processing using the spline curve as a filter output as a signal processing result can be easily performed on the measurement data. Therefore, it is possible to prevent the end-effect at the start point of the measurement data or the end point region of the measurement data, and the shape included in the measurement data without being affected by the follow-up characteristic or the noise component of the long period included in the measurement data. Can be extracted. As a result, it is possible to perform filter processing with good shape following characteristics, and the reliability of measurement data is further improved.
[0012]
  here, MeasureConstant data is one-dimensional time-series data (for example, data obtained by measuring the displacement of the Y axis at predetermined intervals in the X-axis direction for orthogonal X-axis and Y-axis), two-dimensional data (for example, orthogonal X-axis and Y-axis). Free-curve data in the XY plane defined by the axis), three-dimensional data (for example, free-space curve data in the XYZ space defined by the orthogonal X-axis, Y-axis, and Z-axis), or defined by the radius and angle Measurement data such as polar coordinates.
  Further, inputting measurement data along a measurement path includes inputting measurement data along a predetermined scanning direction, and inputting measurement data by measuring the surface of the object to be measured.
[0014]
  furtherSince the weight decreases as the distance of the measurement data from the spline curve calculated by the weighted spline filter equation increases, robust spline filter processing that is not affected by abnormal data included in the measurement data becomes possible. That is, the weight of the measurement data away from the spline curve is small, and the weight of the measurement data close to the spline curve is increased to repeatedly obtain the spline curve. Then, the spline curve gradually approaches the original shape component (for example, the shape true value of the object to be measured) included in the measurement data. The last spline curve at the time when it is determined that the weight has converged is obtained as a shape component having a sufficiently small error with respect to the original shape component. As a result, extremely good robust spline filter processing can be performed.
[0015]
  Further, the present invention provides the measurement dataIsIt is preferable that the measurement data includes two or more orthogonal components, and the distance of the measurement data is determined based on the sum of squares of each component.
[0016]
According to the present invention, when the measurement data is two-dimensional data or three-dimensional data in Cartesian coordinates, the separation amount of the measurement data from the spline curve is the component for each axis (for example, the X-axis component and the Y-axis component). , The Z-axis component, etc.) is determined based on the sum of squares, so that the distance can be easily calculated. Therefore, it becomes easy to determine the weight of each measurement data.
[0017]
In the present invention, it is preferable that the convergence determination step determines that the weight has converged when the change in the weight determined in the weight adjustment step becomes a predetermined value or less.
[0018]
According to the present invention, it is possible to determine that the weight has converged when the change in the weight in the iterative loop processing is equal to or less than a predetermined value. Processing time can be shortened. Furthermore, since it can be determined that the error with the original shape component included in the measurement data is sufficiently small for the spline curve at the time when the change in weight becomes equal to or less than a predetermined value, extremely good robust spline filter processing can be performed. It will be.
[0019]
In the present invention, the output step includes a weight update step for updating the weight to 1 when the weight for the measurement data exceeds a predetermined value, and a spline filter for obtaining a spline filter output based on the updated weight. It is preferable to include a re-output calculation step and a signal processing result output step of outputting the spline filter output in the spline filter re-output calculation step as a signal processing result.
[0020]
According to the present invention, when the weight at the time when it is determined that the weight has converged in the convergence determination step exceeds a predetermined value, the weight is updated to 1, the spline filter output is obtained again, and the result is obtained as the signal processing result. Can be output as In other words, when it is determined that the weight has converged by repeating the weight adjustment step and the spline filter output calculation step, the measurement data at the point where the weight exceeds a predetermined value is regarded as valid data and the weight is updated to 1. After that, the spline filter output is obtained again. Then, the robust spline filter calculation for the measurement data can be performed more reliably. Since the result is output as a signal processing result, a spline curve having a sufficiently small error with respect to the original shape component included in the measurement data can be obtained. As a result, it is possible to perform robust spline filtering with good shape tracking.
[0021]
  Further, the present invention provides the measurement dataIsWhen the spline filter output is obtained including two or more orthogonal components, it is preferable to obtain the spline filter output based on a result of performing weighted spline filter calculation for each component.
[0022]
According to the present invention, even if the measurement data is two-dimensional data or three-dimensional data, the result of the weighted spline filter calculation for each axis component (for example, the X-axis component, the Y-axis component, etc.) Since the spline filter output can be obtained based on this, the calculation process can be simplified even for a complex curve, and the robust spline filter calculation process time for the measurement data can be shortened.
[0023]
In the measurement data input step according to the present invention, it is preferable that the measurement data is input at predetermined intervals along the measurement path.
[0024]
According to the present invention, in addition to inputting measurement data along a predetermined scanning direction, measurement data is input at a predetermined interval along the measurement path even when measuring data is input by copying the surface of the object to be measured. Since data is input, for example, the shape change point (for example, a change point from a straight line to a circular arc or a step boundary point) can be captured more accurately than when measurement data is input at a predetermined interval in the X-axis direction. I can do it. That is, it is possible to prevent errors in shape determination and the like, and to input measurement data with high reliability.
[0025]
In the present invention, it is preferable that the measurement data input step includes a step of deleting locally separated singularity data with respect to the measurement data.
[0026]
According to the present invention, for example, by generating strong induction noise using a power device in a factory or the like as a noise source, locally protruding and separated data included in measurement data (for example, data on both sides) Since data with extremely different values at only one location can be deleted in advance as obvious singularity data, the reliability of the robust spline filter processing is further improved.
[0027]
A signal processing program according to the present invention causes a computer to execute the signal processing method described above. The recording medium of the present invention is characterized in that the signal processing program is recorded so as to be readable by a computer. And the signal processing apparatus of this invention makes a computer run said signal processing program, It is characterized by the above-mentioned.
[0028]
According to such a configuration, if a computer having a CPU (central processing unit) or a memory (storage device) is incorporated and a program is configured to cause the computer to execute each process, for example, weight adjustment, convergence determination, etc. In addition, various parameters can be easily changed including determination of the separation amount according to the dimension of the measurement data. Then, the recording medium on which the program is recorded may be directly inserted into the computer, and the program may be installed in the computer. A reading device that reads information on the recording medium is externally attached to the computer, and the program is installed on the computer from the reading device. May be. The program may be supplied and installed on the computer via a communication line such as the Internet, a LAN cable, a telephone line, or wirelessly.
DETAILED DESCRIPTION OF THE INVENTION
(First embodiment)
First, the weighted spline filter will be described.
As an example, n is the number of data, y_k(K = 0, 1,..., N-1) is the measurement data, and the spline function is s, the sum of squares of the residual with the measurement data,
[Expression 1]

The energy of the spline,
[Expression 2]

This is achieved by minimizing under the condition of minimizing. That is, the spline filter is
[Equation 3]

Is realized by obtaining a spline function s that minimizes I (s). Where λ is Lagrange's undetermined multiplier.
[0029]
Now w_kIf (k = 0, 1,..., N-1) is a weight for the residual at each measurement point, an expression corresponding to a weighted spline filter,
[Expression 4]

Is obtained.
[0030]
Here, the spline function s is discretized at a constant pitch, and the second term is
[Equation 5]

Then,
[Formula 6]

[0031]
It becomes. However,
[Expression 7]

And Therefore, the value s of the discretization spline that minimizes I (s)_kIs
[Equation 8]

Satisfied.
[0032]
In Equation (6), a weighted spline filter is defined by a spline function that minimizes I (s).
[0033]
Here, considering the matrix representation of the weighted spline filter for non-periodic measurement data, the boundary condition is
[Equation 9]

Then,
[Expression 10]

So
## EQU11 ##

The matrix representation of the weighted spline filter for aperiodic data is
[Expression 12]

Given in.
[0034]
However,
[Formula 13]

It is.
[0035]
Next, considering the matrix representation of the weighted spline filter for periodic measurement data, the periodic boundary condition formula is
[Expression 14]

Then,
[Expression 15]

Because
[Expression 16]

The matrix representation of the weighted spline filter for periodic data is
[Expression 17]

Given in.
[0036]
Here, the amplitude characteristic and phase characteristic of the spline filter are examined.
Spline filter formula with weight W = I (unit matrix),
[Expression 18]

The z^-1Means a delay of Δx, and expressed in z-transform,
[Equation 19]

It becomes.
[0037]
The transfer function H (z) of the spline filter is
[Expression 20]

Given in. To examine the amplitude and phase characteristics,
[Expression 21]

After all,
[Expression 22]

It becomes.
[0038]
here,
[Expression 23]

Because
[Expression 24]

And the amplitude characteristic is
[Expression 25]

It becomes.
[0039]
On the other hand, the phase characteristic is
[Equation 26]

Thus, it can be seen that the spline filter is a phase compensation filter.
[0040]
As an example, the cut-off frequency ω = ω_CWhen realizing a 50% attenuation filter, the amplitude characteristics
[Expression 27]

Thus, the constant α is given by the following equation.
[Expression 28]

Cut-off frequency ω = ω_CFig. 5 shows the transfer characteristics (amplitude characteristics and phase characteristics) of the 50% attenuation filter.
[0041]
Next, the solution of the weighted spline filter defined in this way is examined.
Matrix representation of weighted spline filter,
[Expression 29]

Left-side coefficient matrix of
[30]

Is a symmetric matrix.
[0042]
Therefore, if M is decomposed into a lower triangular matrix L and a diagonal matrix D using the modified Cholesky method (using the fact that the matrix M is a sparse matrix, the matrix can be decomposed very efficiently. Yes,)
[31]

And the weighted spline filter is
[Expression 32]

It is expressed.
[0043]
here,
[Expression 33]

given that,
[Expression 34]

It becomes.
[0044]
Here, since L is a lower triangular matrix, X can be easily obtained. further,
[Expression 35]

From this relationship, S can be easily obtained from the obtained X.
In actual application,
[Expression 36]

The matrix M can be singular.
[0045]
Therefore, it is ideally solved by the singular value decomposition method. However, when the singular value decomposition method is used, a large-capacity storage device and a large amount of calculation processing time are required. However, when applying to actual measurement data, it is very rare that the matrix M becomes singular, and it is assumed that the measurement data itself has a problem when the matrix M is singular. Is done. Therefore, in the present invention, even when the matrix M is singular, by applying the Gill-Murray modified Choleskey method that can output some kind of answer, the computational efficiency can be improved. Ensure both security and singular matrix countermeasures.
[0046]
As described above, since the weighted spline filter supported by the solution is derived, the robust spline filter is realized by repeatedly performing the calculation process until the convergence condition is satisfied while updating the weight W.
FIG. 1 is a flowchart showing the first processing procedure, and FIG. 2 is a functional block diagram of an apparatus for executing robust spline processing. In this process, first, a measurement data input step for inputting measurement data and a selection step (ST3) for selecting a weighted spline filter equation are executed.
[0047]
In the measurement data input step, step ST1 in which the measurement data is input from the measuring device or the like by the input means 1 and stored in the storage device 2 such as a computer, and the singular point data locally separated from the stored measurement data. Step ST2 of deleting by the singular point data deleting means 3 is executed.
Here, it is assumed that the measurement data is one-dimensional time series data measured by a roughness measuring machine. That is, for example, in a surface roughness measuring machine or the like, when the probe is moved in one direction (x direction), the roughness data y is acquired at a predetermined pitch in the x direction. Whether or not the data is singularity data can be easily determined by whether or not the distance from the least square curve of the measurement data is not less than a predetermined value and not more than a predetermined section width. .
[0048]
Thereafter, in the selection step ST3, the determination means 4 determines whether the measurement data is aperiodic or periodic, and selects a weighted spline filter equation according to this determination. More specifically, it is determined whether the equation (12) or the equation (17) is used depending on whether the measurement data is aperiodic or periodic.
Next, initialization processing (ST4) is performed. Here, as shown in the figure, the initial value S of the output value of the spline filter processing with W = I (unit matrix) is set.⁰(Non-robust spline filter calculation).
Next, measured data Y and S^m(M represents a repetition step.) The weight W is adjusted by the weight adjusting means 5 in the manner described later.^m(ST5).
[0049]
Thereafter, in the spline filter output calculation means 6, a weighted spline filter,
[Expression 37]

To spline filter output S^{m + 1}Is obtained (ST6).
Here, the convergence determination unit 51 performs weight determination (ST7), which will be described later, and if the convergence condition is not satisfied, m is updated (m = m + 1) (ST10), and the weight W is again determined.^mIs adjusted (ST5).
[0050]
If the convergence condition is satisfied (ST7: YES), the iterative process is terminated and the output value S of the robust spline filter^m(ST8), the spline curve is output to the output means 7.
In the above processing, the weight W^mAs a method of determining by adjusting (ST5), the adaptive biweight method is used as follows.
[Formula 38]

[0051]
Where σ is the standard deviation of the residual,
[39]

[Formula 40]

And
[0052]
Further, as the convergence condition in ST7, the process is repeated when the change in weight is sufficiently small and the following equation is satisfied.
[Expression 41]

[0053]
FIG. 3 shows an example in which the signal processing method by the robust spline filter processing in the first embodiment is performed on the one-dimensional time series data. Here, for the measurement data with spike noise added, both the spline curve resulting from the normal spline filter processing and the spline curve resulting from the robust spline filter processing of the present invention are superimposed and displayed. is there. As is apparent from this figure, the result of the spline filter is subject to a change due to spike noise, whereas the result of the robust spline filter provides a spline curve along the original shape. Further, as can be seen from FIG. 3A, the followability with respect to a shape having a gentle undulation is also good.
[0054]
According to this method, the following effects can be expected.
(1) Since the spline filter can be easily made robust, deformation at the measurement data start point or measurement data end point region can be prevented, and it is not affected by the follow-up to the long-term waviness component included in the measurement data or the noise component. Since the shape included in the measurement data can be extracted, it is possible to perform a filtering process with good shape tracking, and the reliability of the measurement data is further improved.
(2) Since the locally separated singularity data included in the measurement data can be deleted, the reliability of the robust spline filter processing is further improved.
[0055]
(3) Since the weight decreases as the distance of the measurement data from the spline curve calculated by the weighted spline filter equation increases, robust spline filter processing that is not affected by abnormal data included in the measurement data is possible. Become.
(4) Since it can be determined that the weight has converged when the change in the weight in the iterative loop processing is equal to or less than a predetermined value, unnecessary processing due to the iterative loop can be prevented, and the robust spline filter calculation processing time can be shortened.
[0056]
(Second Embodiment)
Next, a second processing procedure for realizing a robust spline filter will be described. This processing procedure is the same as the first processing procedure, but the calculation formula used is different.
That is, the weighted spline filter equation,
[Expression 42]

Transform
[Equation 43]

And
[0057]
Here, in repeat step m,
(44)

Is used.
In addition to the effects (1) to (4) of the first processing procedure, the following effects can be expected from the characteristics of the second processing procedure.
[0058]
(5) left side coefficient matrix,
[Equation 45]

Since they always have the same value in the repetition step, the robust spline filter calculation processing time as a whole may be shortened.
[0059]
(Third embodiment)
Next, as a third embodiment of the signal processing method of the present invention, a signal processing method for measurement data that is two-dimensional data measured two-dimensionally will be described. Here, the measurement data which is two-dimensional data is obtained by measuring the contour curved surface of the object to be measured at a predetermined pitch with a constant Z coordinate in, for example, a three-dimensional measuring machine (x, y). Means coordinate values. Or, it means data when a figure drawn in a plane is read by a scanner. That is, in the first embodiment, the processing target is only the y coordinate, whereas in the third embodiment, both the x coordinate and the y coordinate are the processing targets.
The basic configuration of the third embodiment is the same as that of the first embodiment, but is characterized by an expression corresponding to Expression (6), which is a starting expression for obtaining the spline curve s.
[0060]
In the third embodiment, the measurement data (x_k, Y_k) And this measurement data (x_k, Y_k) On the spline curve s (s_x(X_k, Y_k), S_y(X_k, Y_k)) And a spline curve that minimizes the sum of squares of the distances in the X and Y directions. That is, a spline function s that minimizes I (s) expressed by the following equation under the above-mentioned incidental conditions is obtained.
[0061]
[Equation 46]

[0062]
However, in the second term on the right side, the Laplacian quadratic approximation is expressed as follows.
[0063]
[Equation 47]

[0064]
Then, the weighted spline filter described in the first embodiment is executed for each x component and y component (see (Equation 37)).
Here, for the constant α, the sampling pitch Δl along the measurement path and the cutoff wavelength λ_c'Is given by the following equation.
[0065]
[Formula 48]

[0066]
Then, a spline filter for deriving a spline curve in each section related to the two-dimensional measurement data is realized.
Further, in the robust spline filter that repeats the process until the weight W is updated and the convergence condition (Expression 41) is satisfied, (y in (Expression 38)_k-S_k ^m) Is the distance between two points given by the following equation. That is, measurement data (x_k, Y_k) And this measurement data (x_k, Y_k) On the spline curve s (s_x(X_k, Y_k), S_y(X_k, Y_k)).
[0067]
[Formula 49]

[0068]
The convergence of the weight W calculated by (Expression 38) applying (Expression 49) is determined by (Expression 41). When the weight W has converged, the output value S^mA spline curve corresponding to the measurement data is obtained from (spline function). This spline curve is output to the output means.
[0069]
FIG. 4A shows a comparison between input data obtained by adding spike noise to the normal leaf line and that obtained by performing spline processing and that subjected to robust spline processing. From FIG. 4A, it can be seen that the mere spline processing is dragged by spike noise, whereas the robust spline processing provides a robust (robust) result with suppressed spike noise. FIG. 4 (B) shows the input data with spike noise added to the airfoil and the result of applying spline processing and the result of applying robust spline. The results are the same as in FIG. 4 (A). is there.
[0070]
In the third embodiment, in addition to the effects (1) to (5) in the first and second embodiments, the following effects are further obtained.
(6) When the measurement data is two-dimensional data in Cartesian coordinates, the separation amount of the measurement data from the spline curve is based on the sum of squares of components for each axis (for example, X-axis component, Y-axis component, etc.). Therefore, the distance can be easily calculated. Therefore, it becomes easy to determine the weight of each measurement data.
[0071]
(7) Even if the measurement data is two-dimensional data, a spline filter output is obtained based on the result of weighted spline filter calculation for each axis component (for example, X-axis component, Y-axis component, etc.). Therefore, even for a complicated curve, the calculation process can be simplified, and the robust spline filter calculation process time for the measurement data can be shortened.
[0072]
(8) Even when measuring the object to be measured in a two-dimensional plane to obtain two-dimensional data and inputting this as measurement data, the measurement data is input at predetermined intervals along the measurement path. For example, a shape change point (for example, a change point from a straight line to an arc or a boundary point of a step) can be captured more accurately than when measurement data is input at predetermined intervals in the X-axis direction. That is, it is possible to prevent errors in shape determination and the like, and to input measurement data with high reliability.
[0073]
(Fourth embodiment)
Next, as a fourth embodiment according to the signal processing method of the present invention, a signal processing method for measurement data which is three-dimensional data measured three-dimensionally will be described. Here, the measurement data that is the three-dimensional data means (x, y, z) coordinate values obtained by measuring the surface of the object to be measured at a predetermined pitch in a three-dimensional measuring machine, for example. That is, in the first embodiment, the processing target is only the y-coordinate, whereas in the fourth embodiment, three of the x-coordinate, y-coordinate, and z-coordinate are the processing targets.
The basic configuration of the fourth embodiment is the same as that of the first embodiment, but is characterized by an equation corresponding to equation (6), which is a starting equation for obtaining the spline curve s.
[0074]
In the fourth embodiment, measurement data (x_k, Y_k, Z_k) And this measurement data (x_k, Y_k, Z_k) On the spline curve s (s_x(X_k, Y_k, Z_k), S_y(X_k, Y_k, Z_k), S_z(X_k, Y_k, Z_k)) And the spline curve that minimizes the sum of squares of the distances in the X, Y, and Z directions. That is, a spline function s that minimizes I (s) expressed by the following equation under the above-mentioned incidental conditions is obtained.
[0075]
[Equation 50]

[0076]
However, in the second term on the right side, the Laplacian quadratic approximation is expressed according to the third embodiment.
Then, the weighted spline filter described in the first embodiment is executed for each of the x component, the y component, and the z component (see (Expression 37)). For the constant α, the sampling pitch Δl and the cutoff wavelength λ along the measurement path in the three-dimensional space._c′ Is defined according to (Equation 48).
[0077]
Then, a spline filter for deriving a spline curve in each section related to the three-dimensional measurement data is realized.
Further, in the robust spline filter that repeats the process until the weight W is updated and the convergence condition (Expression 41) is satisfied, (y in (Expression 38)_k-S_k ^m) Is the distance between two points given by the following equation. That is, measurement data (x_k, Y_k, Z_k) And this measurement data (x_k, Y_k, Z_k) On the spline curve s (s_x(X_k, Y_k, Z_k), S_y(X_k, Y_k, Z_k), S_z(X_k, Y_k, Z_k)).
[0078]
[Formula 51]

[0079]
Then, the convergence of the weight W calculated by (Expression 38) applying (Expression 51) is determined by (Expression 41). When the weight W has converged, the output value S^mA spline curve corresponding to the measurement data is obtained from (spline function). This spline curve is output to the output means.
[0080]
In addition to the effects (1) to (5) in the first embodiment and the second embodiment, the fourth embodiment has the following effects.
(9) The effects (6) to (8) in the third embodiment can be further exerted on the three-dimensional data. Therefore, even if the measurement data is three-dimensional data, the calculation load can be reduced without increasing the calculation processing time of the robust spline filter.
[0081]
(Modification 1)
A modification of the signal processing method of the present invention will be described. In the first embodiment, an example in which the spline curve at the time when the convergence is determined is output as it is as a signal processing result, but in this modification, the spline curve is obtained again and the result is output as the signal processing result. .
[0082]
FIG. 6 shows a modification of the spline curve output (ST9) of FIG.
Here, first, the acquired output value S^mIs input (ST91). Thereafter, it is determined whether or not to perform recalculation (ST92). For example, the operator may specify YES when it is desired to obtain the signal processing result with high accuracy, and NO when determining that the result has already been obtained with sufficient accuracy. Alternatively, it can be specified in advance.
When no recalculation is performed (NO), the output value S^mThe spline curve is output by the output means 7. When recalculation is performed (YES), the weight exceeding the predetermined value set in advance is updated to 1 (ST93). That is, measurement data having a weight exceeding a predetermined value is determined to be valid data, and the contribution to the spline calculation process is set to 100%.
Thereafter, a weighted spline filter calculation is performed based on the updated weight to obtain an output (ST94). The spline curve obtained here is output from the output means 7 as a signal processing result (ST95).
[0083]
Since this modification can also be implemented in the first to fourth embodiments, in addition to the effects (1) to (9), the following effects can be achieved.
(10) When the weight at the time when it is determined that the weight has converged in the convergence determination step exceeds a predetermined value, the weight is updated to 1, a spline filter output is obtained again, and the result is output as a signal processing result. be able to. That is, when it is determined that the weight has converged by repeating the weight adjustment step and the spline filter output calculation step, the measurement data at the point where the weight exceeds a predetermined value is regarded as valid data and the weight is set to 1. Since the spline filter output can be obtained again after the update, the robust spline filter calculation for the measurement data can be performed more reliably. Since the result is output as a signal processing result, a spline curve having a sufficiently small error with respect to the original shape component included in the measurement data can be obtained, so that robust spline filter processing with good shape following capability is possible. Become.
[0084]
While the present invention has been described with reference to a preferred embodiment, the present invention is not limited to this embodiment, and modifications can be made without departing from the scope of the present invention.
For example, not limited to these embodiments, three-dimensional roughness data, measurement data by a contour shape measuring machine, data measured by a roundness measuring machine, shape data measured by a three-dimensional measuring machine, an image measuring machine The present invention can be implemented with any of the data measured in (1).
[0085]
Whether the measurement data collection is a contact type sensor or a non-contact type sensor, it is not limited to the surface property data of the object to be measured. Even if it exists, this invention can be implemented.
Furthermore, in the present embodiment, the measurement data has been described only when it is once stored in the storage device. However, the present invention is applicable even when calculation processing is performed in real time each time measurement data is collected. Can be implemented.
[0086]
Furthermore, the signal processing method of the present invention may be a signal processing program that causes a computer to execute the signal processing program, and the signal processing program is stored in a form that can be executed by various computers using a portable storage medium such as a CD-ROM. can do. The signal processing program may be in a compiled format that is translated into a machine language or in an interpreted format that is translated into an intermediate language.
[0087]
In addition, a signal processing apparatus can be configured by causing a computer to execute the signal processing program. In other words, the measurement data input step is executed, the measurement data input means is executed, the selection step is executed, the selection means is executed, the initialization step is executed, the initialization means is executed, the weight adjustment step is executed, and the weight adjustment means is executed. The spline filter output calculating step is executed to configure the spline filter output calculating means, the convergence determining step is executed to execute the convergence determining means, and the output step is executed to configure the output means, thereby configuring the signal processing apparatus.
[0088]
【The invention's effect】
As described above, according to the present invention, a signal processing method capable of performing filter processing using a robust spline filter can be performed at high speed and with high accuracy.
[Brief description of the drawings]
FIG. 1 is a flowchart showing a signal processing procedure in a first embodiment according to a signal processing method of the present invention.
FIG. 2 is a functional block diagram of an apparatus that performs signal processing in the first embodiment.
FIG. 3 is a diagram comparing the result of spline processing and the result of robust spline processing for one-dimensional time-series data in the first embodiment.
FIG. 4 is a diagram comparing the result of spline processing and the result of robust spline processing in the third embodiment of the present invention.
FIG. 5 is a diagram illustrating transfer characteristics according to a signal processing method according to the present invention.
FIG. 6 is a flowchart showing a modification of the present invention.
[Explanation of symbols]
3 Singularity data deletion means
5 Weight adjustment means
6 Spline filter output calculation means

Claims (10)

In a signal processing method for performing a filtering process on measurement data obtained by measuring the surface property of a measurement object ,
A measurement data input step for inputting the measurement data along a measurement path;
A selection step of determining whether the measurement data is periodic and selecting a weighted spline filter equation according to the determination ;
An initializing step of obtaining an initial value of a spline filter output by giving a weight to the measurement data in a unit matrix;
A weight adjustment step of adjusting and determining a weight for the measurement data;
A spline filter output calculation step for obtaining a spline filter output using the weight determined in the weight adjustment step;
A convergence determination step for determining convergence of the weights;
An output step of outputting a signal processing result based on the spline filter output,
The weight determined in the weight adjustment step is:
The amount of measurement data from the spline curve calculated by the weighted spline filter equation and a variable determined based on the amount of separation are adjusted to be smaller as the amount of separation increases.
When it is determined in the convergence determination step that the weight is non-convergence, the weight is updated, the weight adjustment step and the spline filter output calculation step are repeated, and robust spline filter processing is performed on the measurement data. The signal processing method characterized by giving. The measurement data includes two or more orthogonal components,
The signal processing method according to claim 1, wherein the separation amount of the measurement data is determined based on a sum of squares of each component. The convergence determination step includes:
3. The signal processing method according to claim 1, wherein the weight is determined to have converged when the change in the weight determined in the weight adjustment step is equal to or less than a predetermined value. 4. The output step includes
A weight update step for updating the weight to 1 when the weight for the measurement data exceeds a predetermined value;
A spline filter re-output calculation step for obtaining a spline filter output based on the updated weight;
A signal processing result output step for outputting the spline filter output in the spline filter re-output calculation step as a signal processing result;
The signal processing method according to claim 1, further comprising: The measurement data includes two or more orthogonal components,
5. The signal processing according to claim 1, wherein when the spline filter output is obtained, the spline filter output is obtained based on a result of performing weighted spline filter calculation for each component. Method. In the measurement data input step,
6. The signal processing method according to claim 1, wherein the measurement data is input at predetermined intervals along the measurement path. The measurement data input step includes
7. The signal processing method according to claim 1, further comprising the step of deleting locally separated singularity data with respect to the measurement data.   A signal processing program causing a computer to execute the signal processing method according to claim 1.   9. A recording medium on which the signal processing program according to claim 8 is recorded.   A signal processing apparatus that causes a computer to execute the signal processing program according to claim 8.

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